derivative f(x)=(x^6-4x^2+2)ln(x)

解

導関数

f (x) = (x^{6} - 4 x^{2} + 2) ln (x)

ln (x) (6 x^{5} - 8 x) + \frac{x ^{6} - 4 x ^{2} + 2}{x}

解答ステップ

\frac{d}{d x} ((x^{6} - 4 x^{2} + 2) ln (x))

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{6} - 4 x^{2} + 2, g = ln (x)

= \frac{d}{d x} (x^{6} - 4 x^{2} + 2) ln (x) + \frac{d}{d x} (ln (x)) (x^{6} - 4 x^{2} + 2)

\frac{d}{d x} (x^{6} - 4 x^{2} + 2) = 6 x^{5} - 8 x

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= (6 x^{5} - 8 x) ln (x) + \frac{1}{x} (x^{6} - 4 x^{2} + 2)

\frac{1}{x} (x^{6} - 4 x^{2} + 2) = \frac{x ^{6} - 4 x ^{2} + 2}{x}

= ln (x) (6 x^{5} - 8 x) + \frac{x ^{6} - 4 x ^{2} + 2}{x}